Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions

作者：Sakakibara Koya^*

来源：Japan Journal of Industrial and Applied Mathematics, 2017, 34(1): 177-228.

DOI：10.1007/s13160-017-0241-4

• Method of fundamental solutions
• Charge simulation method
• Potential problem
• Invariance
• Multiply-connected region

The aim of this paper is to develop mathematical theory of the conventional and invariant schemes for the method of fundamental solutions used to solve potential problems in doubly-connected regions. Particularly, we prove that an approximate solution actually exists uniquely under some conditions, and that the error decays exponentially when the boundary data are analytic, and algebraically when they are not analytic but belong to some Sobolev spaces. Moreover, we present results of several numerical experiments in order to show the sharpness of our error estimate.

• 出版日期2017-4